Digital-to-analog (D/A) conversion is the process of converting digital codes into analog signals. Analog-to-digital (A/D) conversion is the complimentary process of converting a continuous range of analog signals into digital codes. Such conversion processes are necessary to interface real-world systems, which typically monitor continuously varying analog signals, with digital systems that process, store, interpret, and manipulate the analog values.
With the increased sophistication of cellular telephones, hand-held camcorders, portable computers, and set-top cable TV boxes, the requirements or performance criteria of D/A and A/D circuits has increased. These and other similar applications generally have low power and long battery life requirements. They may also have high speed and high resolution requirements.
One example of an application for a high performance digital-to-analog converter (DAC) is converting a digital signal, representing a desired modulated output signal in a digital transmitter, to an analog signal with a relatively high intermediate frequency. The relatively high intermediate frequency is desirable so that filtering subsequent mixer images is easier after the analog signal is mixed to the final radio frequency.
In the past it has been difficult to obtain a useful, high intermediate frequency signal from a low cost DAC because of the sinx/x filtering characteristic typical of a sample-and-hold action of the DAC that reduces the amplitude of signals with higher intermediate signals.
FIG. 1 illustrates a prior art application of a DAC used to convert a modulated digital intermediate frequency signal into an analog signal suitable for transmission, such as radio frequency transmission. As shown in FIG. 1, digital signal source 20 provides a modulated digital intermediate frequency signal that represents data to be transmitted. Such data may represent voice, video, or a data file that may be software, or some sort of user data such as a document. The modulated digital intermediate frequency signal is typically a serial stream of digital bits that comprise symbols that have been processed for transmission over a channel. Such processing may include interleaving and error coding to improve the efficiency of transmission over the channel.
The output of digital signal source 20 is coupled to a digital-to-analog converter (DAC) 22. DAC 22 converts digital codes into a signal having discrete analog voltages.
The output of DAC 22 is coupled to the input of lowpass filter 24, which attenuates all but the first baseband image in the analog signal output by DAC 22. Lowpass filter 24 may be implemented with a surface acoustic wave device or other frequency selective device, which are well known in the art.
Following the output of lowpass filter 24, the analog signal is mixed up to an intermediate frequency (IF) by mixer 26 having an input from a local oscillator with frequency F.sub.L01. Note that this mixing function may be thought of as a "frequency translating function" because the frequency of a signal component may be translated, up or down, to a new frequency. In one embodiment, an IF (local oscillator frequency F.sub.L01) near 200 MHz is used. Mixer 26 may be implemented with an integrated circuit sold under part number JYM-20H, available from Mini-Circuits, Brooklyn, N.Y.
Mixer 26 is followed by bandpass filter 27 and second mixer 28 that mixes the intermediate frequency output of mixer 26 up to the final transmission frequency, which may be a radio frequency (RF). In one embodiment, an RF (local oscillator frequency F.sub.L02) near 2 GHz is used. Mixer 28 may also be implemented with part number JYM-20H, available from Mini-Circuits. Bandpass filter 27 selects, or passes, one of the mixing product signals produced by mixer 26.
Using two mixing stages with a first stage IF at 200 MHz provides a 400 MHz frequency spacing between the mixing product signal pair at the output of mixer 28. This rather large spacing permits the use of an economic, low order filter following mixer 28 (not shown) to select one of the signals in the mixer image pair for final amplification and transmission.
The output of mixer 28 may then be forwarded to an amplifier (not shown) for amplifying a signal to a level that may be transmitted over a channel. The channel may be a radio frequency channel, in which case the signal is transmitted wirelessly from a transmitter to a receiver. Alternatively, the channel may be in another medium, such as a coaxial cable or an optical fiber. In such alternative media, signals output by DAC 22 may still be mixed up to another frequency for the purpose of frequency division multiplexing.
Referring now to FIG. 2, there is depicted a graph of frequency components, and their amplitudes, that are present in the analog signal output by DAC 22.
In graph 40, amplitude is plotted against frequency. On the frequency axis, F.sub.L is the sample frequency of digital signal source 20. A plurality of signal components, including baseband signal component 42 and aliased signal components 44, are shown at various frequencies. Each signal component is in a separate Nyquist band. A first Nyquist band is shown at reference numeral 46 and contains baseband signal component 42. If digital signal source 20 provides a complex digital signal, first Nyquist band 46 is twice as large, extending from zero to the sample frequency F.sub.L. Nyquist bands having frequencies higher than the frequency of the first Nyquist band are referred to as "super-Nyquist bands." These super-Nyquist bands are shown at reference numerals 48.
The amplitude of aliased signal components 44 is determined by a filtering characteristic of DAC 22. Filtering characteristic 50, shown in FIG. 2 as a dotted line, has the shape of the mathematical function six/x. Such a filtering function is typical of a DAC having a sample-and-hold output signal. Thus, amplitudes of aliased signal components 44 are determined by the value of the filtering characteristic function at the particular frequency of the aliased signal component.
Although signal components 42 through 44 have been represented in graph 40 as having a single frequency, these signal components may have some finite bandwidth because the signals may have several frequency components spanning such a bandwidth.
In one embodiment of the prior art, F.sub.L may equal 100 MHz. At the output of DAC 22, lowpass filter 24 selects baseband signal 42 and filters out aliased signal components 44. Mixers 26 and 28, together, mix baseband signal 42 up to a 2 GHz frequency, which may be 20 times the frequency of F.sub.L. Two mixers are typically required because at the transmission frequency a mixer image needs to be filtered from the transmitted signal and it is difficult to filter such a mixer image when its frequency is close to the frequency of the transmitted signal. By using two mixers and mixing in two stages, the transmitted signal and its mixer image are separated in frequency, which makes the mixer image filter easier to implement because it can be designed with fewer poles.
Because filters with a higher number of poles are more difficult to design and implement, an upsampler may be used prior to the DAC in order to separate the baseband signal from the aliased signal components. This allows the use of a filter with fewer poles to filter the aliased signal components from the baseband signal.
As shown in FIG. 3, upsampler 60 and lowpass digital filter 62 are used to process the signal output by digital signal source 20 prior to being input to DAC 66. Upsampler 60 performs a "zero stuffing" function wherein one digital symbol is input into upsampler 60 and, for example, three digital symbols are output from upsampler 60. Of these output symbols, one symbol is the originally input symbol and the following symbols are zero valued symbols. In the examples shown in FIGS. 3 and 4, upsampler 60 upsamples by a factor of M, where M equals three.
Lowpass digital filter 62 filters out aliased signal components output by upsampler 60 in the new, larger, first Nyquist band 64. Note that the Nyquist bands in FIG. 4 are larger, or broader, because of the upsampling function.
The output of lowpass digital filter 62 is input into DAC 66, which operates, in this example, at sampling frequency F.sub.H, which is three times faster than DAC 22 shown in FIG. 1. The graph shown in FIG. 4 shows the frequency components of the output of DAC 66. Baseband signal component 42 is located in first Nyquist band 64. Aliased signal components 44 are located in super-Nyquist bands 68. Note that the Nyquist bands in FIG. 4 are three times as wide as the Nyquist bands shown in FIG. 2. The wide Nyquist bands are a result of upsampler 60 and DAC 66 operating three times as fast.
The output of DAC 66 is filtered by lowpass filter 70 in order to remove aliased signal components 44 in super-Nyquist bands 68. Following lowpass filter 70, mixers 26 and 28 frequency translate baseband signal component 42 up to the desired transmission frequency. Note that lowpass filter 70 may be implemented with a filter having fewer poles than lowpass filter 24 (see FIG. 1). This makes lowpass filter 70 less expensive and easier to build. Fewer poles are needed because baseband signal 42 is spaced further apart in frequency from aliased signal components 44 as shown by the difference between FIGS. 2 and 4.
While the digital signal processing shown in FIG. 3 allows for a simpler lowpass filter at the output of the DAC, the circuit in FIG. 3 still requires two mixers in order to translate the DAC output to the desired transmission frequency. Therefore, a need exists in the prior art for an improved method and system for processing a digital signal for analog frequency transmission that eliminates the need for two mixers for mixing an output of a DAC up to a desired transmission frequency and permits the use of a simpler, lower order filter, to filter a mixer image to produce a signal for transmission.